From the hardware and JTAG protocol side, yes. You need to find a programmer and software that supports both AVR and ARM, though, and that can cope with multiple devices on a JTAG chain.
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starblueDec 16 '12 at 10:26

You'll be hard pressed to find a programmer that does both for the simple reason that the pinout is different. The next challenge would be finding software that supports both architectures. For instance, OpenOCD supports many different chips. However, AVR isn't one of them.
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embedded.kyleDec 17 '12 at 15:14

@ChrisStratton Significant? Maybe not from a construction standpoint. Worth mentioning? I thought so. Since many use the same size connector but have different connection arrangement including vendor specific pins, I felt it was useful to point it out in case the OP wasn't aware.
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embedded.kyleJan 18 '13 at 13:46

1 Answer
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If you use the vendors programming tools the chances are that although they will work in a chain each vendor will only be able to program it's chip.

However there are vendor agnostic 'universal' programming tools, e.g. OpenOCD, which is open source. Commercial ones exist too. Often the work involved in configuring the universal too to work with all the chips is more work then using each vendor tool one at a time.

Most vendor tools allow you to create SVF (Serial Vector Format) files, these files tell third party universal tools and SVF players how to program each of the chips in the chain without the actual tool having to have built in knowledge of how to program the chip.